Physics 
EOS 
Rocket Science 
Stage 2 Saturn V. no gravity 
Stage 2 — The rocket has already jettisoned the Stage 1 frame and has coasted for 4.4 seconds. v_{exhaust} = 4220 m/s R = 1190 kg/s t_{final} = 360 s m^{0}_{fuel } = 0.428x10^{6} kg m_{initial} = m_{final}^{Stage 1}— m_{jettison}^{Stage 1 } = 0.73x10^{6} kg — 0.136x10^{6} kg = 0.594x10^{6} kg m_{final} = 0.594x10^{6} kg — 0.428x10^{6} kg = .166x10^{6} kg = m_{body } v_{initial } for Stage 2 is v_{final} of Stage 1—use the Stage 1 result: 3275 m/s—no gravity 
**6.5 second coast period between second and third stages; displacement given by x_{coast} = t_{coast} v_{final} 
Stage 2 Results and Graphs — no gravity 
Let’s dispense with gravity and look at the results if the Saturn V rocket were to be unfettered. 
webpages and Eos image copyright 2020 M Nealon 
Data for individual stages. 
Stage 2 Notes v_{final } = 8650 m/s = 19,300 miles/hour a(t_{initial}) = .9 g’s a(t_{final}) = 3.1 g’s x(t_{final}) = 1950 km = 1210 miles After the Stage 2 burn, the rocket jettisons 0.0432x10^{6} kg. 
Stage 3 Saturn V. no gravity Stage 3 occurs in two burns: the first burn puts the rocket into Earth orbit, the second is the translunar injection. Let’s live dangerously and burn it all in one go! . . . why not!* 
Stage 3 Notes v_{final } = 17,100 m/s = 38,200 miles per hour; NASA says the speed at this point would be around 24,500 miles/hour (11,000 m/s). At this rate the rocket would arrive at the moon in hours, not 3 days! The reason it takes so long to arrive at the moon is because the rocket slows down. There’s the influence of gravity again! a(t_{final}) = 5.1 g’s — upwards of 10 g’s becomes painful x(t_{final}) = 3400 miles 
Stage 3 Results and Graphs 
Stage 3 — Total burn 477 seconds. v_{exhaust} = 4630 m/s R = 216 kg/s t_{final} = 477 s m^{0}_{fuel } = 0.103x10^{6} kg m_{initial} = m_{final}^{Stage 2}— m_{jettison}^{Stage 2 } = 0.166x10^{6} kg — 0.0432x10^{6} kg = 0.123x10^{6} kg m_{final} = 0.123x10^{6} kg — 0.103x10^{6} kg = 0.020x10^{6} kg = m_{body } v_{initial } for Stage 3 is v_{final} of Stage 2 — 8650 m/s 
*Same results either way. 
Page 1 Momentum Derivation of the Rocket Equation Thrust
Page 2 Speed of the Rocket During the Burn
Page 3 Rocket Acceleration Position as a Function of Time
Page 4 Gravity
Page 5 Saturn V Data Stage 1 Calculation
Page 6 Saturn V Stage 2, Stage 3 Calculations
Page 7 Saturn V Photo Gallery
Page 8 Saturn V Photo Gallery
Page 9 Equation Review 
6 —Stage 2 —Stage 3 
Stage 2 equations – no gravity 
Stage 3 equations – no gravity 
m_{initial} (x10^{6 }kg) 
m_{final} (x10^{6} kg) 
v_{initial} (m/s) 
v_{final} (m/s) 
a(t=0) (m/s^{2}) 
a(t_{final}) (m/s^{2}) 
x(t_{final}) (km) 
x_{coast}^{**} (km) 
Final Altitude (km) 
0.594 
.166 
3275 
8650 
8.45 
30.2 
1950. 
56.2 
2010. 










m^{0}_{fuel} Fuel Mass (x10^{6}kg) 
T Thrust (x10^{6}N) 
t_{final} Burn Duration (s) 
v_{exhaust} Exhaust Velocity (m/s) 
R Burn Rate (kg/s) 
Frame Mass to jettison (X10^{6}kg) 
First stage 
2.04 
33.4 
150 
2456 
13600 
0.136 
Second stage 
.428 
5.02 
360 
4220 
1190. 
0.0432 
Third stage a 
0.0356 
1.00 
165 
4630 
216. 
— not yet 
b 
0.0674 
1.00 
312 
4630 
216. 
0.0174 
m_{initial} (x10^{6 }kg) 
m_{final} (x10^{6} kg) 
v_{initial} (m/s) 
v_{final} (m/s) 
a(t=0) (m/s^{2}) 
a(t_{final}) (m/s^{2}) 
x(t_{final}) (km) 
X_{coast} (km) 
Final Displacement (km) 
0.123 
0.020 
8650 
17,100 
8.1 
50. 
5,560 
all the way to the moon 
5,560 










m^{0}_{fuel} Fuel Mass (x10^{6}kg) 
T Thrust (x10^{6}N) 
t_{final} Burn Duration (s) 
v_{exhaust} Exhaust Velocity (m/s) 
R Burn Rate (kg/s) 
Frame Mass to jettison (X10^{6}kg) 
Third stage a 
0.0356 
1.00 
165 
4630 
216. 
— not yet 
b 
0.0674 
1.00 
312 
4630 
216. 
0.0174 
Third stage in one burn 
0.103 
1.00 
477 
4630 
216. 
0.0174 